






from __future__ import annotations

from fractions import Fraction

def        UpperCAmelCase__		(						lowerCamelCase_       :       int   ,  lowerCamelCase_       :       int				):
			return (
			    num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
			)

def        UpperCAmelCase__		(						lowerCamelCase_       :       int				):
			__a						:  int									=     []
			__a						:  int									=     1_1
			__a						:  List[Any]									=     int('1' + '0' * digit_len				)
			for num in range(lowerCamelCase_   ,  lowerCamelCase_				):
						while den <= 9_9:
									if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
												if is_digit_cancelling(lowerCamelCase_   ,  lowerCamelCase_				):
															solutions.append(f'''{num}/{den}'''				)
									den += 1
						num += 1
						__a						:  Union[str, Any]									=     1_0
			return solutions

def        UpperCAmelCase__		(						lowerCamelCase_       :       int = 2				):
			__a						:  Optional[Any]									=     1.0
			for fraction in fraction_list(lowerCamelCase_				):
						__a						:  int									=     Fraction(lowerCamelCase_				)
						result *= frac.denominator / frac.numerator
			return int(lowerCamelCase_				)


if __name__ == "__main__":
							print(solution())







def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     int = 10**9)   ->       int:






							'''simple docstring'''





							__UpperCamelCase      :  int       =   1
							__UpperCamelCase      :  Any       =   2

							__UpperCamelCase      :  Dict       =   0
							__UpperCamelCase      :  Any       =   0
							__UpperCamelCase      :  List[Any]       =   0
							while perimeter <= max_perimeter:
														perimeters_sum += perimeter

														prev_value += 2 * value
														value += prev_value

														__UpperCamelCase      :  Optional[int]       =   2 * value + 2 if i % 2 == 0 else 2 * value - 2
														i += 1

							return perimeters_sum


if __name__ == "__main__":
		print(f"{solution() = }")